To solve the equation
[tex]\[
-9(x+3)+12=-3(2 x+5)-3 x,
\][/tex]
follow these steps:
1. Distribute the constants on both sides:
On the left side, distribute [tex]\(-9\)[/tex] over [tex]\((x + 3)\)[/tex]:
[tex]\[-9(x + 3) = -9x - 27.\][/tex]
Adding [tex]\(12\)[/tex] gives:
[tex]\[-9x - 27 + 12 = -9x - 15.\][/tex]
So the left side simplifies to:
[tex]\[-9x - 15.\][/tex]
On the right side, distribute [tex]\(-3\)[/tex] over [tex]\((2x + 5)\)[/tex]:
[tex]\[-3(2x + 5) = -6x - 15.\][/tex]
Adding [tex]\(-3x\)[/tex] gives:
[tex]\[-6x - 15 - 3x = -9x - 15.\][/tex]
So the right side simplifies to:
[tex]\[-9x - 15.\][/tex]
2. Compare the simplified equations:
Therefore, after simplification, the equation becomes:
[tex]\[-9x - 15 = -9x - 15.\][/tex]
3. Analyze the equation:
Both sides of the equation are identical. This implies that the equation holds true for any value of [tex]\(x\)[/tex].
Therefore, the correct statement about this equation is:
C. The equation has no solution.
